If memory serves, Jaguar made some Imperial (normal) size wheels for the XJ40 in the same style. If you keep an eye on ebay for a set of 16" Jag wheels, you should eventually come up with a set. Then you can have them refurbed and new 16" tyres fitted.
Check the manufacture date on your Avon tyres, if they're over 5 years old i wouldn't use them at all. I had a brown trouser moment in my S Type not long after getting it when the steering failed to respond due to the (near new in terms of tread) Pirelli P6000 just did not grip - they were ~10 years old at the time.
I now run a set of new Maxxis Premitra HP5 tyres, similar to the P6000 in tread pattern, feel and probably better in grip having driven on new P6000s some years back. Would definitely recommend them!